The value of x is given as follows:
x = 16.2.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.First we must obtain the bases, splitting the figure into two separate similar triangles, with equivalent dimensions given as follows:
16 and y.30 and 34 - y.Hence the proportional relationship used to obtain the value of y is given as follows:
16/y = 30/(34 - y)
Hence:
30y = 16(34 - y)
46y = 544
y = 544/46
y = 11.83.
Hence the bases are:
11.83 and 34 - 11.83 = 22.17.
Applying the geometric mean theorem, the value of x is given as follows:
x = sqrt(11.83 x 22.17)
x = 16.2.
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The parabola y=√x-4 (principal square root) opens: down left Right up
The parabola \(y = √(x - 4)\) opens upward.
The parabola y = √(x - 4) represents the square root function of x minus 4. To determine the direction in which the parabola opens, we examine the behavior of the square root function.
The square root function (√x) returns non-negative values for non-negative inputs. Since the expression inside the square root, (x - 4), must be non-negative for real solutions, we have x - 4 ≥ 0. Solving this inequality, we find x ≥ 4.
This means that the parabola is defined for x values greater than or equal to 4. As we increase x from 4, the value of √(x - 4) will also increase. Therefore, the graph of the parabola opens upward.
The parabola \(y = √(x - 4)\) opens upward.
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Hey guy don’t you hate does people that said here is the link to your answer
Answer:
Thats not the way to give an answer..should write it properly
its just similar to..someone asked your name and you say this is the link and you give him the link of the ppt you made of your name
Can anyone help me with this answer please
Answer:
Step-by-step explanation:
f(x)=x² +1
What is f(f(x))?
Step-by-step explanation:
Plug
\( {x}^{2} + 1\)
for x.
\(( {x}^{2} + 1) {}^{2} + 1\)
Note that
\((a + b) {}^{2} = 2ab\)
So we have
\( {x}^{4} + 2 {x}^{2} + 2\)
Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function
Based on the definition of the functions, the value of x if f(x) = g(x) is 3
How to determine the value of x?The equations of the functions are given as
f(x) = -2x + 4
g(x) = 2x - 8
It should be noted that the above equations are linear equations
From the question, we understand that the functions are equal
This means that, we have the following equation
f(x) = g(x)
Substitute the known values in the above equation
So, we have the following equation
-2x + 4 = 2x - 8
Collect the like terms in the above equation
So, we have
2x + 2x = 8 + 4
Evaluate the like terms in the above equation
So, we have
4x = 12
Divide both sides by 4
x = 3
Hence, the value of x such that the equations are equal is 3
Graph the functionsSee attachment for the graph of the functions
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Find the value of L that Will Maximize the profit Q=L²e^0.01L
The minimum profit occurs at L = 0, where Q = 0.
To find the value of L that maximizes the profit Q = L²\(e^{(0.01L)\).
We need to differentiate Q with respect to L and find the critical points where the derivative equals zero.
Then we can determine whether each critical point is a maximum or a minimum by examining the second derivative.
Testing for critical points:Q = L²\(e^{(0.01L)\)
Q' = \(2Le^{(0.01L)\) + \(0.01 L^2e^{(0.01L)\)
= 0(2L + 0.01L²) \(e^{(0.01L)\)
= 0L (critical point) or 200 \(e^{(0.01L)\)
= 0 (extraneous, ignore)
2L + 0.01L² = 0L(2 + 0.01L) = 0L = 0 or L = -200 (extraneous, ignore)
The only critical point is at L = 0.
Testing for maximum or minimum:Q'' = \(2e^{(0.01L)\) + 0.02Le^(0.01L) + 0.0001L²\(e^{(0.01L)Q''(0)\)
= \(2e^{(0)\) = 2Since Q''(0) > 0,
The critical point at L = 0 is a minimum.
Therefore, there is no value of L that maximizes the profit.
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The values of L that will maximize the profit are 0 and -200
Finding the value of L that will maximize the profitFrom the question, we have the following parameters that can be used in our computation:
\(Q = L\²e^{0.01L\)
Differentiate the function
So, we have
\(Q' = \frac{L \cdot (L + 200) \cdot e^{0.01L}}{100}\)
Set the equation to 0
\(\frac{L \cdot (L + 200) \cdot e^{0.01L}}{100} = 0\)
Cross multiply
\(L \cdot (L + 200) \cdot e^{0.01L} =0\)
When expanded, we have
L = 0, L + 200 = 0 and \(e^{0.01L} =0\)
When solved for L, we have
L = 0 and L = -200
Hence, the values of L are 0 and -200
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Please help math experts thank you have a great day
Answer:
a - 2
Step-by-step explanation:
All you have to do is divide 3a by 3 and divide -6 by 3
3a ÷ 3 is a-6 ÷ 3 is -2∴ The answer is a - 2
Hope this helps!
Suppose a life insurance company sells a ​$190,000 ​one-year term life insurance policy to a 19​-year-old female for ​$290. The probability that the female survives the year is 0.999563. Compute and interpret the expected value of this policy to the insurance company.
Answer:
The expected value of this policy to the insurance company is $206.97
Step-by-step explanation:
Probability that Person doesn't die = 0.999563. Profit = Revenue - Cost; Profit = $290 - 0 = $290
Probability that Person dies = 1 - 0.999563 = 0.000437. Profit = Revenue - Cost; Profit = $290 - $190,000 = -$189,710
Expected Value E(X) = ∑xp(x)
E(X) = $290*(0.999563) + (-$189,710* 0.000437)
E(X) = $289.87327 - $82.90327
E(X) = $206.97
Thus, the expected value of this policy to the insurance company is $206.97
What is percent 10 1/4 of 66?
Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation. What are the values a, b, and c in the following quadratic equation? -3x^2 -5x +9 =0
Answer:
The quadratic equation is in the standard form: ax^2 + bx + c = 0. To use the quadratic formula to find the solutions, we need to identify the values of a, b, and c in the equation:
a is the coefficient of the x^2 term, which is -3 in this case.
b is the coefficient of the x term, which is -5 in this case.
c is the constant term, which is 9 in this case.
Therefore, the values of a, b, and c in the quadratic equation -3x^2 - 5x + 9 = 0 are:
a = -3
b = -5
c = 9
I need help please.....
Answer:
C
Step-by-step explanation:
Move the decimal to the right 4 times
For the following exercises, evaluate the function f at the indicated values.
a. f(-3) b. f(2) c. f(-a) d. -f(a)
4. f(x)=2x-5
5. f(x)=−5x²+2x−1
6. f(x)=x-1-x+1
After we evaluate the function f at the indicated values the results are
a. (4) −11, (5) −52, (6) 0
b. (4) -1, (5) −17, (6) -5
c. (4) −2a−5, (5) −5a² −2a−1, (6) −3+a
d. (4) −2a+5, (5) 5a² −2a+1, (6) 3+a
What is function?A relation in which there is only one possible pairing of each x and each y is called a function. It should be noted that while the reverse is true, the same y can be paired with different x. Vertical and horizontal lines are the only types of linear equations that are not functions.
Lets evaluate the function a. f(-3)
4. f(-3) = 2(-3)-5
= −11
5. f(-3) = −5(-3)²+2(-3)−1
= −52
6. f(-3) = -3-1-(-3)+1
= 0
Lets evaluate the function b. f(2)
4. f(2) = 2(2)-5
= −1
5. f(2) = −5(2)²+2(2)−1
= −17
6. f(2) = -3-1-(2)+1
= −5
Lets evaluate the function c. f(-a)
4. f(-a) = 2(-a)-5
= −2a−5
5. f(-a) = −5(-a)²+2(-a)−1
= −5a² −2a−1
6. f(-a) = -3-1-(-a)+1
= −3+a
Lets evaluate the function d. -f(a)
4. -f(a) = -(2(a)-5)
= −2a+5
5. -f(a) = -(−5(a)²+2(a)−1)
= 5a² −2a+1
6. -f(a) = -(-3-1-(a)+1)
= 3+a
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PLEASE PLEASE HELP ASAP PLEASE PHOTO ATTACHED ABOVE PLEASE HELP
Answer:
is y= 8-2x/3
Step-by-step explanation:
the 2x/3 is a fraction
determine if the function f(x)=3^(2x-3) is exponential
An exponential function gives a variable raised to the power of x, where the variable is a positive real number
Yes, \(\underline{f(x) = 3 ^{(2 \cdot x - 3)}}\) is an exponential function
Reason:
An exponential function is a function that can be written in the form;
f(x) = eˣ
Where;
e = Euler's number, which is the number approximately 2.71828
In the general form, an exponential number is a number given in the form;
f(x) = a·bˣ
Where;
b = A positive real number
The given function; \(f(x) = 3 ^{(2 \cdot x - 3)} = \dfrac{3^{2\cdot x}}{3^3} = \dfrac{1}{27} \times 9^x\) is an exponential function
Where;
a = \(\dfrac{1}{27}\)b = 9Therefore, the correct response is; Yes, \(f(x) = 3 ^{(2 \cdot x - 3)}\) is an exponential function
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Sort the polynomials according to whether they are prime or non-prime.
Prime Polynomials
6x³-5x²+2x-14
12-18+8²-12
6x² +9x2 +10x+15
12x²-3x+4x+7
Non-Prime Polynomials
Answer: first, second and fourth are primes, the third is not-prime.
Hope it helps :)
can someone help me
Answer:
no answer
Step-by-step explanation:
An assembly worker is making 3-legged and 5-legged stools. She has 67 legs to use in all for the day's work. What is the largest number of 3- legged stools she can make and still use all the legs to make 5-legged stools with the rest of the legs?
Answer:
Step-by-step explanation:
let number of 5 legs=x
so 67-5x =multiple of 3
x=1,67-5=62 not divisible by 3
x=2,67-5×2=57 ÷3=19
so he can make 19 three -legged table and 2 five -legged table.
What is the answer to −517÷97?
5.3 ? I think.
The mixed number ver is -5 32/97
Find the solution to the system of equations given below using elimination by addition.
5x + 20y = 60
x + 3y = 9
Please refer to the attachment for the answer and explanation. Hope it helps!!:))
help meeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeee
The estimate of the number of students studying abroad in 2003 is 169 and the estimate of the number of students studying abroad in 2018 is 433
a. Estimate the number of students studying abroad in 2003.
The function is given as:
y = 123(1.065)^x
Where x represents years from 1998 to 2013
2003 is 5 years from 1998.
This means that
x = 5
Substitute the known values in the above equation
y = 123(1.065)^5
Evaluate the exponent
y = 123 * 1.37008666342
Evaluate the product
y = 168.520659601
Approximate
y = 169
Hence, the estimate of the number of students studying abroad in 2003 is 169
b. Assuming this equation continues to be valid in the future, use this equation to predict the number of students studying abroad in 2018.
2018 is 20 years from 1998.
This means that
x = 20
Substitute the known values in the above equation
y = 123(1.065)^20
Evaluate the exponent
y = 123 * 3.52364506352
Evaluate the product
y = 433.408342813
Approximate
y = 433
Hence, the estimate of the number of students studying abroad in 2018 is 433
what double fact can you use to add 5+6
Answer:
They can use counters or their fingers, but they can also use doubles facts. If they know 5 + 5 = 10, they know that the sum of 5 + 6 will be one more. Thus, 5 + 6 = 11. Practice solving other doubles-plus-one facts together, such as 3 + 4, 7 + 8, and 9 + 8.
Answer:
Step-by-step explanation:
11
A farmer is planting vegetables on his field. The farmer has planted 24 seeds so far, which is 40% of it's capacity. What is the maximum number of seeds the farmer is able to plant on his field?
Answer: the answer is 104
Step-by-step explanation:
Answer:
104
Step-by-step explanation:
Determine whether the following relation represents a function. Give the domain and range for the relation. StartSet (7 comma 2 )comma (5 comma negative 4 )comma (3 comma 3 )comma (negative 4 comma negative 4 )EndSet
Answer:
is a functiondomain: {-4. 3. 5. 7}range: {-4, 2, 3}Step-by-step explanation:
Given:
{(7, 2), (5, -4), (3, 3), (-4, -4)}
__
The domain is the set of first numbers:
{7, 5, 3, -4} . . . domain
The range is the set of second numbers:
{2, -4, 3} . . . range
No domain values are repeated, so this relation is a function.
1 + 1 I'm confusedddddddddddddddddddddddddddddddddddddddddd
Answer:
its 2 homie
Step-by-step explanation:
1+1 equals 2 one thing plus another equals the next number.
Jennifer started a lawn mowing business and borrowed $85 to buy materials. Nicholas started a babysitting business and borrowed $60 to buy materials. Which statement correctly shows who has the greater debt?
Answer:
Jennifer because she would make less but spent more on supplies
Step-by-step explanation:
Answer: The answer is D! Jennifer, |-85| > |-60|
Step-by-step explanation: I did the quiz hope everyone does great ^^
HELP PLEASE<33 IM NOT SURE HOW TO DO THIS!
Answer:
Step-by-step explanation:
1b. <
1c. =
1d. >
2c. n=6
3. Yes
4. 4
5. 5 1/3
6. 2 3/5
Explain how the distributive property helps us multiply the following polynomials and why and how the final products differ:(a + b)^2,(a – b)^2,(a - b)(a + b)
Answer:
because you have to distrubute the 2 to the letters inside the () or else youll get a diff answer thats wrong
Step-by-step explanation:
1. Sally uses 312 cups of flour for each batch of cookies.
How many cups does she need to make 4 batches of cookies?
A girl can do her homework in 1.5 hours. How long would It take her twin brother to do the same homework alone if together they do it in 40 minutes?
Answer:
72 minutes
Step-by-step explanation:
in minutes,
1/90 + 1/x = 1/40
x = 72
Normal distribution has a mean of 98 and standard deviation of 6. What is P(x > 104)
The value οf P(x > 104) is 0.1587 οr apprοximately 15.87%.
What is Prοbability?Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.
Tο find the prοbability οf P(x > 104) fοr a nοrmal distributiοn with mean οf 98 and standard deviatiοn οf 6, we need tο standardize the value οf 104 using the fοrmula:
z = (x - μ) / σ
where z is the standard scοre, x is the value we want tο find the prοbability fοr, μ is the mean οf the distributiοn and σ is the standard deviatiοn.
Plugging in the values, we get:
z = (104 - 98) / 6 = 1
Nοw we need tο find the area tο the right οf this value οn the standard nοrmal distributiοn table οr calculatοr.
Using a standard nοrmal distributiοn table οr calculatοr, we find that the area tο the right οf z = 1 is 0.1587.
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